Results 41 to 50 of about 2,299 (159)
Journal of Function Spaces, 2020 In this paper, we consider the evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under the Rauch condition,
Hicham Mahdioui +2 more
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Optimizing condition numbers [PDF]
, 2009 In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function.
Jane J. Ye, Lewis A.S., Pierre Maréchal
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Minimization of nonsmooth integral functionals
International Journal of Mathematics and Mathematical Sciences, 1992 In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from ...
Nikolaos S. Papageorgiou +1 more
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Complexity, 2020 This paper is devoted to the investigation of optimality conditions for approximate quasi weak efficient solutions for a class of vector equilibrium problem (VEP).
Yameng Zhang, Guolin Yu, Wenyan Han
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Reconstruction of the Clarke Subdifferential by the Lasry–Lions Regularizations
Journal of Mathematical Analysis and Applications, 2000 Suppose that \(f\) is a locally Lipschitz function defined on a Hilbert space, which satisfies the growth condition \[ -{C\over 2}(\|x\|^2+ 1)\leq f(x)\leq {C\over 2}(\|x\|^2+ 1). \] It is proved that the Clarke subdifferential \(\partial f(x)\) (of \(f\) at \(x\)) can be represented by the derivatives of its Lasry-Lions regularizations \((f_\lambda ...
Georgiev, Pando Gr., Zlateva, Nadia P.
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Nonlinear Analysis, 2019 In this paper, we mainly consider a control system governed by a Hilfer fractional evolution hemivariational inequality with a nonlocal initial condition.
Yatian Pei, Yong-Kui Chang
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Evolution inclusions with Clarke subdifferential type in Hilbert space
Mathematical and Computer Modelling, 2010 The authors consider the existence of solutions for differential inclusions of the form \[ \begin{aligned} -\dot{x}(t) &\in \partial _{C}\phi (x(t))+G(t,x(t)),\\ x(0) &=x_0\end{aligned}\tag{1} \] in a real, separable Hilbert space \(H\), where \(\partial _{C}\) denotes the Clarke subdifferential.
Qin, Sitian, Xue, Xiaoping
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Clarke subgradients of stratifiable functions [PDF]
, 2006 We establish the following result: if the graph of a (nonsmooth) real-extended-valued function $f:\mathbb{R}^{n}\to \mathbb{R}\cup\{+\infty\}$ is closed and admits a Whitney stratification, then the norm of the gradient of $f$ at $x\in{dom}f$ relative to
Bolte, J. +3 more
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Second-order subdifferential calculus with applications to tilt stability in optimization [PDF]
, 2011 The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full
Mordukhovich, B. S., Rockafellar, R. T.
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Characterization of the monotone polar of subdifferentials
, 2013 We show that a point is solution of the Minty variational inequality of subdifferential type for a given function if and only if the function is increasing along rays starting from that point.
Lassonde, Marc
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